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- anonymous

let f(x) = lxl is f continuous at x = 0 why ????????

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- anonymous

let f(x) = lxl is f continuous at x = 0 why ????????

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- dumbcow

f is continuous because there are no gaps in the graph, in other words the point x=0 is defined
-> f(0) = |0| = 0

- anonymous

this is exact question i wrote ,,,, i also dont know ,,,,,

- dumbcow

For a counter example imagine f(x) =|x| for x<0 and x>0 but f(x) = 1 for x=0 This means the y value jumps up 1 when you go from .00001 to 0 there is a gap

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- dumbcow

make sense??

- anonymous

yes ,,,

- anonymous

thnx

- anonymous

Do you know about limits?

- anonymous

yes

- anonymous

The function is continuous if \(\lim_{x \rightarrow c^+} f(x) = \lim_{x \rightarrow c^-} f(x) = f(c) \)

- anonymous

i am new with limits ,,,

- anonymous

As x gets closer and closer to c either from the -infinity or +infinity sides, the function must approach the value f(c) in order to be continuous
For f(x) = |x| we see that the limit from the left is approaching f(0)=0 along the y=-x line.
From the right we see it's approaching f(0) = 0 along the y=x line.
Also the value of the function at x = 0 is 0 which is the value being approached from the left and the right. Therefore it is continuous about 0. (in fact it is continuous everywhere).

- anonymous

k ,,,, thnx a lot ,,,,,,,,,

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